1. CHAPTER 6 Digital Filter Structures
Wang Weilian
School of Information Science and Technology
Yunnan University ~

2. Outline Block Diagram Representation Equivalent Structures
Basic FIR Digital Filter Structures
Basic IIR Digital Filter Structures
FIR Cascaded Lattice Structures
Summary
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3. Block Diagram Representation
Digital filters
The difference equation
A first-order causal LTI IIR digital filter:
Knowing the initial condition y[-1] and the input x[n] for , we can computer y[n] for
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4. Block Diagram Representation
An LTI digital filter can be conveniently represented in block diagram form using the basic building blocks representing the unit delay, the multiplier, the adder and the pick-off nods.
e.g. :
A first-order LTI digital filter
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5. Equivalent Structures
Two digital filter structures is equivalent if they have the same transfer function.
There are a number of methods for the generation of equivalent structures:
( i ) Reverse all paths,
( ii ) Replace pick-off nodes by adders, and vice versa,
( iii ) Interchange the input and the output nodes.
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6. Basic FIR Digital Filter Structures
Direct forms
In the time-domain:
The transfer function:
An FIR filter of order N requires N+1 multipliers and N two-input adders for implementation in general.
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7. Basic FIR Digital Filter Structures
Direct Forms
Direct form FIR structures
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8. Basic FIR Digital Filter Structures
Cascade Form
2L=N unit delays，2L+1=N+1 multipliers，2L=N adders
Cascade form FIR structure
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9. Basic FIR Digital Filter Structures
Linear-Phase FIR Structures
A linear-phase FIR filter of order N
The symmetric impulse response:
The antisymmetric impulse response:
Linear-phase FIR structure
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10. Basic IIR Digital Filter Structures
Direct Forms
An Nth-order IIR digital filter transfer function requires 2N+1 multipliers and 2N two-input adders for implementation in general.
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11. Basic IIR Digital Filter Structures
Direct Forms
Direct form I
Direct form It
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12. Basic IIR Digital Filter Structures
Cascade Realizations
Various different cascade realizations of H(z) can be obtained by different pole-zero polynomial pairings.
Usually, the polynomials are factored into a product of first-order and second-order polynomials.
e.g. :
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13. Basic IIR Digital Filter Structures
Cascade Realizations
Cascade realization of a IIR transfer function
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14. Basic IIR Digital Filter Structures
Parallel Realizations
Making use of the partial-fraction expansion of the transfer function:
The parallel form I:
The parallel form II:
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15. Basic IIR Digital Filter Structures
Parallel Realizations
Parallel realization of a IIR transfer function
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16. FIR Cascaded Lattice Structures
Realization of Arbitrary FIR Transfer Functions
All-Zeros filter:
From fig 6.39:
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17. Summary
The realization of a causal digital transfer function, called structures, are usually represented in block diagram forms that are formed by interconnecting adders, multipliers, and unit delays.
The structure can be analyzed to develop its input-output relationship either in the time-domain or in the transform-domain.
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